In a big test of parliament's willingness to reform itself, MPs will vote tomorrow on whether to let backbenchers take immediate control of most non-ministerial business in parliament, or follow a government call to kick the issue into the long grass.

The reforms were proposed by a committee set up last year by Gordon Brown, chaired by a senior Labour backbencher, Tony Wright, to give parliament greater independence from the executive. They are being sold as a way of restoring parliament's reputation after the expenses scandal.

But the government has tabled the vote for this afternoon in the hope that most MPs will have left for their constituencies.

Harriet Harman, the leader of the house, will propose that a new backbench business committee responsible for organising debates and votes on backbench business should not be set up until after the election, and that the issue should be considered in detail by the procedure committee, which is selected by party whips.

David Cameron's frontbench is also trying to water down the Wright committee plans, proposing that the backbench committee be set up immediately after the election, but only be responsible for allotting 15 days of set-piece debates a year.

The all-party Wright committee proposed three months ago that the new backbench business committee be set up before the election. It would have powers to ensure that backbench motions were not just debated but also voted upon, giving parliament a stronger collective voice independent of the party whips. It would organise the backbench agenda one day a week, tilting the balance in parliament substantially from executive to MPs.

Evan Harris, a Liberal Democrat member of the Wright committee, said: "We have had to battle to get this far, and it is vital that reform-minded MPs do not give up now. In the debate on these reforms last week, there was widespread support, so why are the front benches trying to defer them now?"

Senior backbenchers from all the main parties support setting up the new backbench business committee immediately, including Graham Brady, who is likely to be elected chairman of the Conservative backbench 1922 committee. But it is unclear whether enough backbenchers will turn up tomorrow to vote through the reforms immediately.

Advocates of immediate reform point out that there is little that MPs backing the reforms now will be able to do in the next parliament to ensure momentum is not lost, and that once the proposals are reconsidered by a procedure committee they may lose their bite. A Cameron government might not be keen to cede executive powers to parliament, especially if it only had a small majority.

In theory, the vote is free of government whipping, but in practice frontbenches can heavily influence how MPs vote.

There will be greater unanimity on setting up a separate business committee, of backbenchers and whips, to reform scheduling of government business to ensure amendments to bills, including those passed in the Lords, are fully debated by MPs. At present great tranches are passed without debate. The joint committee would meet once a week and agree a parliamentary timetable that could then be put to a vote of all MPs.

MPs are also likely to back election of select committee members and that select committee chairs should be elected by a secret ballot of all MPs,.

An array of other reforms advanced by Wright has been deferred until after the election.